Oughtred Society Slide Rule History. Slide Rule History Prologue In the 16th Century, engineering design as we know it today, with its emphasis on precise measurements and finely calculated tolerances, is unthinkable. And yet, every scientist, mathematician and alchemist feels that there are basic fundamental mathematical relationships that underpin the natural world. The pre-eminent figures in science both contribute to the creation of the slide rule and make use of it in their work, including Galileo, Napier, Gunter, Oughtred, Newton, Gauss, Watt, Priestley, Fulton, Fuller, Einstein, Fermi, and Von Braun. A quick look at the first five of these men covers the creation and initial evolution of the slide rule. Just Before the Slide Rule Galileo Galilei popularizes the sector at the very end of the 16th Century. The sector is a graduated ruler that uses trigonometric formulae and a caliper to calculate squares, cubes, reciprocals and tangents of numbers. Galileo's design of the sector as a mathematical tool can be seen as the moment when calculation aids cease to be based upon counting and instead exploit the deeper relationships among numbers.

His invention is still in use as a navigation aid in the 20th century … 300 years later. John Napier dramatically advances the understanding of number relationships in 1614 with his invention of logarithms. Since logarithms are the foundation on which the slide rule is built, its history rightly begins with him. His early concept of simplifying mathematical calculations through logarithms makes possible the slide rule as we know it today. Chronology of the Slide Rule Napier himself contributes Napier's Bones in 1617, calculating sticks based on the gelosia, or lattice, multiplication method. In 1620 Edmund Gunter of London makes a straight logarithmic scale and performs multiplication and division on it with the use of a set of dividers, or calipers. In about 1622 William Oughtred, an Anglican minister … today recognized as the inventor of the slide rule … places two such scales side by side and slides them to read the distance relationships, thus multiplying and dividing directly. He also develops a circular slide rule. In 1675 Sir Isaac Newton solves cubic equations using three parallel logarithmic scales and makes the first suggestion toward the use of the cursor.

In 1677, two years after Newton invents the cursor, Henry Coggeshall perfects the timber and carpenter's rule. Newton's cursor fails to catch on at the time. The Coggeshall rule remains in common use 200 years later. His design and its standardization move the slide rule from a tool of mathematical inquiry to specialized applications. Beginning in 1683, Thomas Everard popularizes the gauging rule, used to determine the content of ale, wine and spirits barrels and to calculate the excise tax thereon. This design, first created by William Oughtred in 1633, sees widespread use well into the 19th century. In 1722 John Warner, a London instrument dealer, uses square and cube scales. By 1790 James Boulton and James Watt are modifying slide rules to improve their accuracy and usefulness. By 1799 their Soho slide rule helps to usher in the Industrial Revolution. It facilitates the design and manufacture of their seminal machine, the steam engine.

In 1815 Peter Roget, an English physician (and the author of Roget's Thesaurus), invents a log log scale, which he uses to calculate roots and powers to any number or fraction thereof. It is regarded at the time as a mathematical curiosity. Fifty years later, advances in electrical engineering, thermodynamics, dynamics and statics, and industrial chemistry make these scales so necessary they are rediscovered. In the next fifty years they increase from three, to six, to eight scales on the slide rule, as engineering extends its grip on modern computation. In 1851 a French artillery officer named Amedee Mannheim standardizes a set of four scales for the most common calculation problems. The four scales include two double length, named A & B, for squares and square roots … and two single length, C & D, for multiplication and division. This scale set becomes the basis of slide rule design for the next 100 years and bears his name today. His design and use of a cursor hastens the eventual widespread acceptance of this feature. Early in the 19th century the first slide rules come into use in the United States.

Ex- president Thomas Jefferson has one, and Joseph Priestley recognizes their advantages in his chemistry work, which includes the discovery of oxygen. By 1870, Germany produces two giants of the slide rule world, Dennert and Pape (makers of Aristo), and Faber (later Faber-Castell). The Dennert and Pape contributions of "engine divided" (engraved) scales and the stable deposit of celluloid on wood are revolutionary. The slide rule's importance to the Industrial Revolution, and the impact of the Industrial Revolution upon the slide rule, are demonstrated by the proliferation of designs. From 1625 to 1800, the first 175 years after its invention, a total of 40 slide rule types, including circular and spiral designs, are recorded. The next 100 years, from 1800 to 1899, sees the creation of 250 slide rule types and manufacturers. Over 90 designs are recorded in the first 10 years of the 20th Century.

Cylindrical calculators with extra long logarithmic scales are invented by George Fuller of Ireland in 1878 and Edwin Thacher of New York in 1881. Production of Thacher's calculator is soon taken over by a Hoboken, New Jersey instruments company, Keuffel and Esser, which had previously imported slide rules for sale. A revolutionary linear slide rule construction with scales on both front and back and with a cursor referring to all scales simultaneously is patented in 1891 by William Cox … an invention he calls the "duplex slide rule". It is sold by K&E. Folded scales CF, DF and CIF are put on slide rules about 1900 to reduce the amount of movement and resetting of the slide. Log log scales in three sections appear about 1901, enabling very accurate calculation of powers and roots to any number or fraction. The Slide Rule's Last Century … the 20th Our last century could not have been built without the slide rule, yet its direct evidence is almost totally missing to the uninformed eye. In the United States, this indispensability is seized upon most successfully by Keuffel and Esser.

This firm moves from importing rules in the 1870s, to building a complex calculating instrument (the Thacher Calculator) in the 1880s, to manufacturing their own slide rules in the 1890s. Their contributions are legion, including the CI scale, their fanatical devotion to precision, their use of colored scales and slanting italics to aid in reading direction. A different path to market dominance is adopted in Japan by Jiro Hemmi. Hemmi systematically experiments with both natural base materials and celluloid, settling upon bamboo as the core, and combining this with very modern manufacturing (including celluloid surface lamination), resulting in both high quality and quantity. In the 1960's Hemmi is producing one million slide rules annually. Epilogue The philosophy of engineering moves on. And the triumphs of 20th Century design become limitations for the slide rule. Einstein favors a Nestler slide rule in his work. The approaches to the Golden Gate Bridge and the thrust profile of the Redstone Rocket are designed with simple Rietz based slide rules … E. H.

Lowry's Dietzgen Phillips 1725 and Wernher Von Braun's Nestler 23 respectively. Pickett slide rules provide emergency computational power aboard Apollo missions with their N600-ES model. The Pickett N3 and N4 take their places along with the K&E Decilon and the Post Versalog in designing the F16 fighter airplane. But structural design and first principles in physics both seek answers to how structures will react to changing loads and forces. Wind speeds, tidal friction and interstellar collision all require dynamic computational models, rather than the answer to a static structural problem. Large, slow, obese computing engines designed for these questions give birth to the sleek four-function calculator. K&E's travails with its Analon slide rule model are an excellent example of the change in engineering demands that surpassed the slide rule. The four function electronic calculator is a symptom as much as a cause of this change. Slide rule researchers have estimated that possibly 40 million slide rules were produced in the world in the 20th century alone.

Among these are many types of specialty slide rules developed and made for specific applications such as chemistry, surveying, electricity and electronics, artillery ranging, hydraulics, steam and internal combustion engines, concrete and steel structures, radio and other special fields. The slide rule has a long and distinguished ancestry … from William Oughtred in 1622 to the Apollo missions to the moon ... a span of three and a half centuries … it was used to perform design calculations for virtually all the major structures built on this earth during that long period of our history … an amazing legacy for something so mechanically simple. William Oughtred William Oughtred Location of death: Albury, Surrey, England Cause of death: unspecified Nationality: England Executive summary: Inventor of the slide rule English mathematician, born at Eton, and educated there and at King's College, Cambridge, of which he became fellow. Being admitted to holy orders, he left the university about 1603, and was presented to the rectory of Aldbury, near Guildford in Surrey; and about 1628 he was appointed by the earl of Arundel to instruct his son in mathematics.

He corresponded with some of the most eminent scholars of his time on mathematical subjects; and his house was generally full of pupils from all quarters. It is said that he expired in a sudden transport of joy upon hearing the news of the vote at Westminster for the restoration of Charles II . He published, among other mathematical works, Clavis Mathematica, in 1631, in which he introduced new signs for certain mathematical operations; a treatise on navigation entitled Circles of Proportion, in 1632; works on trigonometry and dialling, and his Opuscula Mathematica, published posthumously in 1676. He is best known for having invented the slide rule (1622), his name being taken by the organization of slide-rule collectors, the Oughtred Society.

Father: Benjamin Oughtred William Oughtred | English mathematician | Britannica.com English mathematician Galileo William Oughtred, (born March 5, 1574, Eton , Buckinghamshire , England —died June 30, 1660, Albury, Surrey ), English mathematician and Anglican minister who invented the earliest form of the slide rule , two identical linear or circular logarithmic scales held together and adjusted by hand. Improvements involving the familiar inner sliding rule came later. William Oughtred, watercolour by George Perfect Harding after an engraving by Wenceslaus Hollar, … Courtesy of the National Portrait Gallery, London Oughtred was educated at Eton College and at King’s College , Cambridge , where he received his bachelor’s degree (1596) and master’s degree (1600). Before his ordainment as an Anglican priest in 1603 and appointment as vicar of Shalford in 1604, Oughtred had already designed (or improved upon) several instruments and composed various works that would be published much later. In 1610 he became rector of Albury, where he remained until his death.

Oughtred was extremely generous in assisting anyone desirous of instruction in mathematics , refusing to accept any remuneration for such instruction. For more than five decades he tutored some of the better-known English mathematicians, such as John Wallis , John Pell, and Seth Ward, as well as numerous teachers of mathematics and instrument-makers who practiced in London. In addition, he kept abreast of the mathematical sciences on the Continent, and either through correspondence or by word of mouth he assisted in the diffusion of French and Italian results among English practitioners. As a clergyman, Oughtred was reluctant to publish on mathematics. However, in 1631 he consented to allow the printing of a small manual that he had utilized in teaching one of his students. The book became famous under the title of Clavis Mathematicae (“The Key to Mathematics”), although it was not an easy text. It compressed much of contemporary European knowledge of arithmetic and algebra into less than 100 pages (in the first edition), while a somewhat obscure style and a penchant for excessive symbolism made the dense text even more challenging. Of the many symbols Oughtred introduced only two are still widely used, “×” for multiplication and “::” for proportion.

Despite its difficulty, the book quickly became one of the most popular mathematics textbooks in 17th-century England. It was often reprinted both in Latin and in the vernacular , and it exerted a formative influence on, among others, the chemist Robert Boyle (1627–91), the architect Christopher Wren (1632–1723), and the mathematician-physicist Isaac Newton (1643–1727). Oughtred’s other writings were published by his students much later, including Trigonometria (1657; “Trigonometry”) and a posthumous collection of tracts, Opuscula mathematica hactenus inedita (1677; “Unpublished Mathematical Papers”). Britannica Stories William Oughtred and the Slide Rule - yovisto Blogyovisto Blog You are here: Home › mathematics › William Oughtred and the Slide Rule William Oughtred and the Slide Rule 1 Tabea Tietz William Oughtred On March 5, 1574, English mathematician and Anglican minister William Oughtred was born.

After John Napier invented logarithms, and Edmund Gunter created the logarithmic scales (lines, or rules) upon which slide rules are based, it was Oughtred who first used two such scales sliding by one another to perform direct multiplication and division; and he is credited as the inventor of the slide rule in 1622. William Oughtred attended the presticous Eton School and enrolled at King’s College Cambridge in 1592. He received his M.A. eight years later and was especially interested in mathematics, even though the field has not been taught extensively at Cambridge back then. Outhred became Episcopal minister in 1603 and became vicar of Shalford one year later. Oughtred was announced rector of Albury in 1610 and took mainly private pupils who received a mathematical education. In 1631, Oughtred published his most impirtant work, ‘Clavis Mathematicae’. In it, he described Hindu-Arabic notations and decimal fractions as well as algebra. Oughtred began to experiment with new mathematical symbols like x for multiplication and :: for proportions.

He used π for the circumference and introduced ‘greater than and less than’ symbols, which were not accepted by the community due to being too hard to remember. The now very familiar < and > were introduced by Harriot. [1] William Oughtred became especailly famous for an early version of the slide rule. Already in 1620, the English clergyman, mathematician, geometer and astronomer Edmund Gunter managed to plot a logarithmic scale along a single straight two foot long ruler. He began to add and substract lengths by using a pair of dividers. The operations used were equivalent to multiplying and dividing. William Oughtred invented a circular slide rule about one decade later. In 1632, Oughtred published Circles of Proportion and the Horizontal Instrument describing slide rules and sundials. [2] It is believed that William Oughtred and Richard Delamain invented the circular slide rule independently from each other. Delamain published his Grammelogia, or the Mathematical ring already in 1630. Big discussions arose over the topic and throughout Oughtred’s later life.

[1] At yovisto you can learn more about “ Why is ‘x’ the symbol for an unknown? ” in a humorous talk by Terry Moore. References and Further Readings: arithmetic and invented the logarithm ` 1622 William - COMP - COMP 206 Arithmetic and invented the logarithm ` 1622 william SCHOOL View Full Document This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: arithmetic and invented the logarithm ` 1622 William Oughtred created the slide rule based on Napiers logarithms. This was the primary calculator used by engineers until the primary calculator used by engineers until the 1960s 2009 Computing for Engineers 47 ` 1612 John Napier used floating point arithmetic and invented the logarithm ` 1622 William Oughtred created the slide rule based on Napiers logarithms.

This was the primary calculator used by engineers the primary calculator used by engineers until the 1960s ` 1642 Blaise Pascal created a machine that could add and subtract, automatically carrying numbers forward 2009 Computing for Engineers 48 9 2009 Computing for Engineers 49 ` 1612 John Napier used floating point arithmetic and invented the logarithm ` 1622 William Oughtred created the slide rule based on Napiers logarithms. This was the primary calculator used by engineers until the 1960s until the 1960 s ` 1642 Blaise Pascal created a machine that could add and subtract, automatically carrying numbers forward ` 1673 Gottfried Leibnitz built a calculator that could multiply as well 2009 Computing for Engineers 50 Joseph-Marie Jacquard invented an automatic loom using punched using punched cards to control patterns in the fabrics.

(Leading to riots against replacing people by machines.) 2009 Computing for Engineers 51 ` 1822 Charles Babbage designed the Difference Engine for computing navigational tables ` 1833 Designed the Analytical Engine that had the basic components used in a modern computer ` 1847-1849 Work carried out on Difference Engine but technology too primitive to build it. In 1991 the Science Museum in London built it 2009 Computing for Engineers 52 Ada Augusta King, Countess of Loveless adds notes and documentation on Analytical Engine. She writes first program.

2009 Computing for Engineers 53 2009 Computing for Engineers 54 10 ` 1890 Hollerith won competition for developing data processing equipment processing equipment for the US Census ` Founded Hollerith Tabulating Company that became IBM in 1924 2009 Computing for Engineers 55 ` 1935-38 Konrad Zuse developed Z-1 and Z- 2 computers using binary arithmetic ` 1936-39 John Vincent Atanasoff and John Berry built ABC computer for solving linear systems in Physics Introduced ALU and systems in Physics. Introduced ALU and rewriting memory. 2009 Computing for Engineers 56 ` 1943 Alan Turing built Colossus used to break German codes encrypted using ENIGMA machine ` 1944 Harvard Mark 1 used to compute artillery and navigation tables and navigation tables 2009 Computing for Engineers 57 ` 1943 Work started on ENIAC at University of Pennsylvania under John Mauchly and J....

COMP COMP 206 - Spring 2009 We are familiar with base-10 numbers Nathan Friedman 2009 Computers use binary, where (2) Computer Structure The Galileo Project Born: Eton, Buckinghamshire, 5 March 1575 Died: Albury, near Guildford, Surrey, 30 June 1660 Dateinfo: Dates Certain 2. Father Occupation: Cleric, Schoolmaster The Rev. Benjamin Oughtred is said to have been a scribe\amanuensis who taught writing. In the accounts the teaching of writing seems to dominate, rather than employment as a scribe. That is, clear handwriting figures in Oughtred's life, and is traced back to his father's influence; I don't think the accounts were trying to describe the father's source of income. No one even talks about the fact he was "the Rev." Mr. Oughtred; I am assuming that this had meaning. His son did follow that calling. No information on financial status. 3.

Nationality Cambridge University, King's College, 1592-1600; B.A., 1596; M.A., 1600. 5. Religion Affiliation: Anglican Oughtred was ordained in 1603 and spent his life as an Anglican clergyman. During the Civil War he was thoroughly royalist in outlook, and would have been sequestered except for influence brought to bear on his behalf. 6. Scientific Disciplines Primary: Mathematics Subordinate: Alchemy Clavis mathematicae, 1631, on arithmetic and algebra, composed for instruction of his pupil, the son of the Earl of Arundel. Circles of Proportion and the Horizontal Instrument, 1632, describing the first slide rules and also sundials. Easy Way of Delineating Dials by Geometry, composed c. 1598, published only in the English Clavis in 1647. Trigonometrie, 1657. Josten is explicit in naming Oughtred an alchemist. 7. Means of Support Fellow of King's College, Cambridge, 1595-1603.

Vicar of Shalford, Surrey, 1604. Rector of Albury, Surrey, 1610-60. Income of ï¿½100. Oughtred was a very active tutor of mathematics: 1620s-60. He himself asserts, and considerable other testimony confirms, that he refused to accept any money in return. Oughtred was a clergyman who was adequately supported in his own view. He does not appear to have aspired for more. Resided in the London house of the Earl of Arundel for some years in 1620s as tutor to the Earl's son. 8. Patronage Types: Aristrocrat, Gentry The Earl of Arundel strongly supported his study, and encouraged him to publish his work. Oughtred dedicated Clavis, composed for the Earl's son, to the Earl. Charles Cavendish is said to have requested the publication urgently; just what his relationship to Oughtred was otherwise is not mentioned. In 1646 Oughtred, a royalist, was about to be sequestered by the Puritan government.

Sir Bulstrode Whitelocke and others exerted influence that allowed him to be spared. The Grand Duke of Florence invited him to Florence and offered him ï¿½500 per annum in 1640s. I will not list this offer, which Oughtred declined; it is probably a myth in any case. 9. Technological Involvement Types: Applied Mathematics, Instruments, Cartography He is generally regarded as the inventor of both the circular and the rectilinear slide rule. He invented a method of calculating logs, and he wrote a short tract on the solution of spherical triangles by the planisphere without the tedious labor of trigonometric calculations. Composed An Easy Way of Delineating Dials by Geometry about 1598. Shortly thereafter he composed a tract on drawing a dial on any plane surface however inclined (published with Circles of Proportion, 1632); in the tract he described an instrument, which he later called the horizontal instrument, a time-showing device and a limited model (on a plane) of the heavens, which allowed the position of the sun to be determined graphically and also made possible the delineation of a dial on any plane surface.

He also wrote a small piece on watchmaking. Oughtred is said also to have practiced as a surveyor. 10. Scientific Societies Memberships: None Informal Connections: Pupils: Seth Ward, Jonas More, Charles Scarborough, John Wallis, Christopher Wren, Mr. Smethwyck, Mr. Austin, Thomas Henshawe, William Forster, Arthur Haughton, Robert Wood, William Gascoigne, and many others. Correspondence with Henry Briggs, Edmund Gunter, Robert Keylway, Dr. Lloyd, and some his (Oughtred's) pupils. Sources Dictionary of National Biography (repr., London: Oxford University Press, 1949-50), 14, 1250-2. O.L. Dick, ed., Aubrey's Brief Lives, (Ann Arbor, 1957), pp.222- 5. Florian Cajori, William Oughtred, a Great Seventeenth-Century Teacher of Mathemetics, (Chicago, 1916). A.J.

Turner, "William Oughtred, Richard Delamain and the Horizontral Instrument in Seventeenth Century England," Annali dell'Istituto e Museo di Storia della Scienze, Firenze, 6.2 (1981), 99-125. Elias Ashmole, 5 vols. ed. with a biographical introduction by C.H. Josten, (Oxford, 1966), 1, 109. Compiled by: Department of History and Philosophy of Science Indiana University William Oughtred - History of the Slide Rule Inventors Expert By Mary Bellis Before we had calculators we had slide rules. The circular (1632) and rectangular (1620) slide rules were invented by Episcopalian minister and mathematician William Oughtred. History of the Slide Rule A calculating tool, the invention of the slide rule was made possible by John Napier's invention of logarithms, and Edmund Gunter's invention of logarithmic scales, which slide rules are based upon. Logarithms According to The Museum of HP Calculators: Logarithms made it possible to perform multiplications and divisions by addition and subtraction.

Mathematicians had to look up two logs, add them together and then look for the number whose log was the sum. Edmund Gunter reduced the labor by drawing a number line in which the positions of numbers were proportional to their logs. William Oughtred simplified things further with the slide rule by taking the two Gunter's lines and sliding them relative to each other thus eliminating the dividers. William Oughtred William Oughtred made the first slide rule by inscribing logarithms on wood or ivory. continue reading below our video Should I Buy my House or Continue to Rent? Before the invention of the pocket or handheld calculator , the slide rule was a popular tool for calculations. The use of slide rules continued until about 1974, after which electronic calculators became more popular. Later Slide Rules Several inventors improved upon William Oughtred's slide rule. 1677 - Henry Coggeshall invented a 2 foot folding slide rule for lumber measure, called the Coggeshall slide rule. 1815 - Peter Mark Roget invented the log log slide rule, which included a scale displaying the logarithm of the logarithm.

1859 - French artillery lieutenant Amédée Mannheim invented an improved slide rule. 1891 - Edwin Thacher introduced a cylindrical slide rule in the United States. The duplex rule was invented by William Cox in 1891. Oughtred biography Version for printing William Oughtred attended Eton School, which although a very famous school was in fact his local school. From there he went to King's College Cambridge, entering in 1592. Three years later he became a Fellow of King's College, received his B.A. in 1596 and his M.A. in the year 1600. It is surprising that although very little mathematics was taught at either Eton or Cambridge at this time Oughtred became passionately interested. He wrote:- ... the time which over and above those usuall studies I employed upon the mathematicall sciences I redeemed night by night from my naturall sleep, defrauding my body, and inuring it to watching, cold, and labour, while most others tooke their rest. Oughtred was ordained an Episcopal minister in 1603.

In 1604 he became vicar of Shalford and later, in 1610, he became rector of Albury. Oughtred took private pupils who came to his house and lived there free of charge while they received mathematical instruction. He had many pupils but the most famous were John Wallis , Christopher Wren and Richard Delamain . Aubrey [ 5 ] gives an interesting description of Oughtred's appearance and lifestyle:- He was a little man, had black haire, and blacke eies (with a great deal of spirit). His head was always working. He would draw lines and diagrams on the dust.... he used to lye a bed till eleaven or twelve a clock, with his doublet on ... studyed late at night, went not to bed till 11 a clock, had his tinder box by him, and on top of his bed-staffe, he had his inke-horne fixed. He slept but little. Sometimes he went not to bed in two or three nights, and would not come downe to meales till he had found out the quaesitum.

Oughtred's most important work, Clavis Mathematicae (1631), included a description of Hindu-Arabic notation and decimal fractions and a considerable section on algebra. He experimented with many new symbols including × for multiplication and :: for proportion. Like all Oughtred's works it was very condensed containing only 88 pages. Oughtred used π in Clavis Mathematicae but not for the ratio of the circumference to the diameter, merely for the circumference. Other notation for greater than and less than proved hard to remember and were not accepted, the familiar > and < being due to Harriot at almost the same time. Oughtred is best known for his invention of an early form of the slide rule. Edmund Gunter (1620) plotted a logarithmic scale along a single straight two foot long ruler. He added and subtracted lengths by using a pair of dividers, operations that were equivalent to multiplying and dividing. In 1630 Oughtred invented a circular slide rule. In 1632 he used two Gunter rulers so that he could do away with the dividers.

He published Circles of Proportion and the Horizontal Instrument in 1632 describing slide rules and sundials. Lesson 1 Readings Return to Lesson 1 A brief history of slide rules John Napier dramatically advances the understanding of number relationships in 1614 with his invention of logarithms. Since logarithms are the foundation on which the slide rule is built, its history rightly begins with him. His early concept of simplifying mathematical calculations through logarithms makes possible the slide rule as we know it today. The ability of logarithms to decompose any number into two parts a base and an exponent  allows the products and dividends of large numbers to be determined by addition and subtraction. Also, using base e (rather than the common base 10) opens the way for tremendous advances in engineering and science, induding the differential calculus. Napier himself contributes Napiers Bones in 1617, calculating sticks based on the geologia (lattice) multiplication method. In 1620 Edmund Gunter of London makes a straight logarithmic scale and performs multiplication and division on it with the use of a set of dividers, or calipers.

In about 1622 William Oughtred, an Anglican minister ... today recognized as the inventor of the slide rule ... places two such scales side by side and slides them to read the distance relationships, thus multiplying and dividing directly. He also develops a circular slide rule . Continue on next page... In 1675 Sir Isaac Newton solves cubic equations using three parallel logarithmic scales and makes the first suggestion toward the use of the cursor. Early slide rules are carefully incised by hand on boxwood or pearwood, of no uniform length, with each bearing the scale divisions of a unique maker. Expensive handcrafted instruments find use among the scientific elite, but this is hardly a sufficient market to sustain slide rule production. Advances in rule design without practical business application are ignored and then forgotten. In 1677, two years after Newton invents the cursor, Henry Coggeshall perfects the timber and carpenters rule. Newtons cursor fails to catch on at the time. The Coggeshall rule remains in common use 200 years later. His design and its standardization move the slide rule from a tool of mathematical inquiry to specialized applications.

Beginning in 1683, Thomas Everard popularizes the gauging rule, used to determine the content of ale, wine and spirits barrels and to calculate the excise tax thereon. This design, first created by William Oughtred in 1633, sees widespread use well into the 19th Century. Throughout the 18th Century, slide rule production and use is mostly English, with limited penetration into other capitalist economies, including France and the Netherlands. Interesting to note is the lack of slide rules and makers in Germany, Switzerland, and Italy ... countries which at this time are producing cutting edge mathematics. Continue on next page... The slide rule delivers the mathematical framework for advances in the industrial arts and for ways of thinking about numbers and their applications in engineering. These discoveries are in turn applied to improvements in the slide rules accuracy, precision, and mass production. In 1722 John Warner, a London instrument dealer, uses square and cube scales. By 1790 James Boulton and James Watt are modifying slide rules to improve their accuracy and usefulness. By 1799 their Soho slide rule helps to usher in the lndustrial Revolution.

It facilitates the design and manufacture of their seminal machine, the steam engine. In the l9th Century the engineer learns that precision to the third decimal place suffices to create superb structures. The slide rule allows such calculation, while its portability encourages design verification and standardization on the job. Modern engineering is invented through the use of the slide rule, itself a design that could only create this impact through modern engineering. In 1815 Peter Roget, an English physician (and the author of Rogets Thesaurus), invents a log log scale, which he uses to calculate roots and powers to any number or fraction thereof. It is regarded at the time as a mathematical curiosity. Continue on next page... Fifty years later, advances in electrical engineering, thermodynamics, dynamics and statics, and industrial chemistry make these scales so necessary they are rediscovered. In the next fifty years they increase from three, to six, to eight scales on the slide rule, as engineering extends its grip on modern computation. During the first half of the 19th Century slide rule use broadens with the extension of education, democracy and free trade. Britain sees tremendous expansion of slide rule types and manufacturers.

Frances revolution of 1795 ushers in a period of extreme mathematical rationality. Results include invention of the metric system, advanced knowledge of the movements of the heavens and earth, and the first requirement that all civil servants demonstrate slide rule proficiency as a part of qualifying exams. In 1851 a French artillery officer named Amedeé Mannheim standardizes a set of four scales for the most common calculation problems. The four scales include two double length, named A & B, for squares and square roots...and two single length, C & D, for multiplication and division. This scale set becomes the basis of slide rule design for the next 100 years and bears his name today. His design and use of a cursor hastens the eventual widespread acceptance of this feature. Continue on next page... Tavernier & Gravet of Paris quickly develops an international reputation for accuracy in production of the Mannheim design . An inverted C scale (CI) and a K scale (for cubes and cube roots) were added later to the face of the rule by others, along with two trigonometry scales (S & T) and a logarithm scale (L) on the back of the slide.

These additions comprise what is often called the Enhanced Mannheim scale set. Belcher Brothers, New York (1821-1876), E.A. Stearns & Co., Vermont (1838-1863) and Stanley Rule & Level Co., Connecticut (1857-1920), add versions of English slide rule designs to their product lines. Palmers Calculator, a circular slide rule, is produced in the United States about 1845. Richardson follows soon after with a steel linear slide rule in 1851. By 1870, Germany produces two giants of the slide rule world, Dennert and Pape (makers of Aristo), and Faber (later Faber-Castell). The Dennert and Pape contributions of engine divided (engraved) scales and the stable deposit of celluloid on wood are revolutionary. Slide rules can now be manufactured with any scale sets desired, to a high degree of precision, with highly visible, reproducible colored faces, allowing accurate calculations to three or four decimal places. The tool exactly corresponds to the revolution in engineering occurring at the same time.

Continue on next page... The slide rules importance to the Industrial Revolution, and the impact of the Industrial Revolution upon the slide rule, are demonstrated by the proliferation of designs. From 1625 to 1800, the first 175 years after its invention, a total of 40 slide rule types, including circular and spiral designs, are recorded. The next 100 years, from 1800 to 1899, sees the creation of 250 slide rule types and manufacturers. Over 90 designs are recorded in the first 10 years of the 20th Century. Cylindrical calculators with extra long logarithmic scales are invented by George Fuller of Ireland in 1878 and Edwin Thacher of New York in 1881. The plates for printing the paper scales of both the Fuller and Thacher calculators are produced by Stanley of London, who probably makes the first Thachers. Production is soon taken over by a Hoboken, New Jersey instruments company, Keuffel and Esser, that had previously imported slide rules for sale.

A revolutionary linear slide rule construction with scales on both front and back and with a cursor referring to all scales simultaneously is patented in 1891 by William Cox...an invention he calls the duplex slide rule . Folded scales CF, DF and CIF are put on slide rules about 1900 to reduce the amount of movement and resetting of the slide. Log log scales in three sections appear about 1901, enabling very accurate calculation of powers and roots to any number or fraction. Continue on next page... Numerous improvements by several manufacturers follow, contributing to the widespread popularity of the slide rule and its many uses in the mathematics of science and engineering, as well as for calculations of all kinds in business and industry. The evidence of the slide rules portable, immediate power stands everywhere around us as the 20th Centurys greatest engineering examples, from the Empire State Building to the Apollo lunar landings. Our last century could not have been built without it, yet its direct evidence is almost totally missing to the uninformed eye. Slide rule researchers have estimated that possibly 40 million slide rules were produced in the world in the 20th Century alone.

Among these are many types of specialty slide rules developed and made for specific applications such as chemistry, surveying, electricity and electronics, artillery ranging, hydraulics, steam and internal combustion engines, concrete and steel structures, radio and other special fields. The slide rule has a long and distinguished ancestry, from William Oughtred in 1622 to the Apollo missions to the moon ... a span of three and a half centuries ... it was used to perform design calculations for virtually all major structures built on this earth during that long period of our history ... an amazing legacy for something so mechanically simple.

Question: What mathematical instrument was invented by William Oughtred in 1622?
Answer: Slide Rule